Achille Giacometti | Università Ca' Foscari Venezia (original) (raw)

Papers by Achille Giacometti

Research paper thumbnail of Computational pipeline to probe NaV1.7 gain-of-function variants in neuropathic painful syndromes

Scientific Reports, 2020

Applications of machine learning and graph theory techniques to neuroscience have witnessed an in... more Applications of machine learning and graph theory techniques to neuroscience have witnessed an increased interest in the last decade due to the large data availability and unprecedented technology developments. Their employment to investigate the effect of mutational changes in genes encoding for proteins modulating the membrane of excitable cells, whose biological correlates are assessed at electrophysiological level, could provide useful predictive clues. We apply this concept to the analysis of variants in sodium channel NaV1.7 subunit found in patients with chronic painful syndromes, by the implementation of a dedicated computational pipeline empowering different and complementary techniques including homology modeling, network theory, and machine learning. By testing three templates of different origin and sequence identities, we provide an optimal condition for its use. Our findings reveal the usefulness of our computational pipeline in supporting the selection of candidates f...

Research paper thumbnail of Proteins -- a celebration of consilience

arXiv (Cornell University), Nov 4, 2021

Proteins are the common constituents of all living cells. They are molecular machines that intera... more Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow from their native state structures and therefore understanding sequence-structure relationships is of fundamental importance. What is quite remarkable about proteins is that their understanding necessarily straddles several disciplines. The importance of geometry in defining protein native state structure, the constraints placed on protein behavior by mathematics and physics, the need for proteins to obey the laws of quantum chemistry, and the rich role of evolution and biology all come together in defining protein science. Here we review ideas from the literature and present an interdisciplinary framework that aims to marry ideas from Plato and Darwin and demonstrates an astonishing consilience between disciplines in describing proteins. We discuss the consequences of this framework on protein behavior.

Research paper thumbnail of Perturbation theory for the Percus-Yevick solution

Research paper thumbnail of Optimal channel networks: A framework for the study of river basin morphology

Water Resources Research, 1993

Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and glo... more Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and global rates of energy dissipation in a continuously fed (in space and time) plane aggregation system reminiscent, and based on the properties, of the planform of three-dimensional natural drainage networks. Geomorphological and fractal properties of OCNs are known from earlier studies by the authors. This paper explores further the structures derived by optimization of energy dissipation rates. Optimality of subnetworks and of basin shapes is investigated as a by-product of competition for drainage. A new perspective on the possible prediction of the width function of a basin network, and hence of its hydrologic response, is obtained by exploiting OCN techniques, requiting only the definition of the outer boundaries of the basin. The interplay between hillslope processes and the development of drainage networks is addressed, aiming at the relative role and the mutual interrelations of geology and optimal organization in the structure of mature fiver basins. Also addressed is the issue of multiscaling and multifractality in the spatial organization of the network. It is concluded that OCN approaches provide a comprehensive framework for the study of the morphology of geophysical structures. !. INTRODUCTION Important processes affect the planimetric structure of drainage basins. Chief among these are the development of channel links by headward growth and branching, migration of valleys and divides, capture processes, and adjustments of junction angles of confluent streams. It has been suggested that after an initial rudimentary drainage network is rapidly created upon strong influence of local topography and structural controls, a more regular, process-controlled, network is slowly formed [e.g., Howard, 1990]. The theoretical treatment of drainage network morphology has been dominated in the last 50 years by two approaches of different nature. One was based on deterministic rules, chiefly opti

Research paper thumbnail of Solvent quality and solvent polarity in polypeptides

Physical Chemistry Chemical Physics

Using molecular dynamics and thermodynamic integration, we report on the solvation process in wat... more Using molecular dynamics and thermodynamic integration, we report on the solvation process in water and in cyclohexane of seven polypeptides (GLY, ALA, ILE, ASN, LYS, ARG, GLU). The polypeptides are...

Research paper thumbnail of Potts-Submission

Research paper thumbnail of Equilibrium and linear transport properties of fluids-Fluids of spherical molecules with dipolarlike nonuniform adhesion: An analytically solvable anisotropic model

Physical Review-Section E-Statistical Nonlinear and Soft Matter Physics, 2008

Research paper thumbnail of Spontaneous dimensional reduction and novel ground state degeneracy in a simple chain model

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new h... more Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first order transition from a high temperature random coil phase to a highly unusual low temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures (we call these PoSSuM -- Planar Structures with Secondary Motifs) in the novel phase and protein native state structures.

Research paper thumbnail of Local symmetry determines the phases of linear chains: a simple model for the self-assembly of peptide

We discuss the relation between the emergence of new phases with broken symmetry within the frame... more We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric constraint that non-consecutive beads cannot overlap, and with a pairwise attractive square well potential accounting for the hydrophobic effect and promoting compaction. We then discuss the consequences of the successive breaking of spurious symmetries. First, we allow the partial interpenetration of consecutive beads. In addition to the standard high temperature coil phase and the low temperature collapsed phase, this results in a new class of marginally compact ground states comprising conformations reminiscent of α-helices and β-sheets, the building blocks of the native states of globular proteins. We then discuss the effect of a further symmetry breaking of the cylindrical symmetry on attaching a side-sphere to the backbone beads along the ne...

Research paper thumbnail of Bridging and depletion mechanisms in colloid-colloid effective interactions: A reentrant phase diagram

A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres ... more A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres represent the solvent and the solute, respectively, is introduced. The solute-solute and solvent-solvent interactions are of hard-sphere type, while the solute-solvent interactions are of sticky-hard-sphere type with tunable degrees of size nonadditivity and stickiness. Two particular and complementary limits are studied using analytical and semi-analytical tools. The first case is characterized by zero nonadditivity, lending itself to a Percus-Yevick approximate solution from which the impact of stickiness on the spinodal curves and on the effective solute-solute potential is analyzed. In the opposite nonadditive case, the solvent-solvent diameter is zero and the model can then be reckoned as an extension of the well-known Asakura-Oosawa model with additional sticky solute-solvent interaction. This latter model has the property that its exact effective one-component problem involves onl...

Research paper thumbnail of Theory and simulation studies of self-assembly of helical particle

This is the unedited authors' version of Chapter 3 appearing in the following book: Self-Asse... more This is the unedited authors' version of Chapter 3 appearing in the following book: Self-Assembly Systems: Theory and Simulations Ed. Li-Tang Yan John Wiley & Sons, Ltd, Chichester, pp. 53-84 (2017)

Research paper thumbnail of Left or right cholesterics? A matter of helix handedness and curliness

We have investigated the relationship between the morphology of helical particles and the feature... more We have investigated the relationship between the morphology of helical particles and the features of the cholesteric (N^∗ ) phase that they form. Using an Onsager-like theory, applied to systems of hard helices, we show that the cholesteric handedness and pitch depend on both the pitch and the curliness of the particles. The theory leads to the definition of pseudoscalars that correlate the helical features of the phase to the chirality of the excluded volume of the constituent particles.

Research paper thumbnail of Phase diagram of heteronuclear Janus dumbbells

Using Aggregation-Volume-Bias Monte Carlo simulations along with Successive Umbrella Sampling and... more Using Aggregation-Volume-Bias Monte Carlo simulations along with Successive Umbrella Sampling and Histogram Re-weighting, we study the phase diagram of a system of dumbbells formed by two touching spheres having variable sizes, as well as different interaction properties. The first sphere (h) interacts with all other spheres belonging to different dumbbells with a hard-sphere potential. The second sphere (s) interacts via a square-well interaction with other s spheres belonging to different dumbbells and with a hard-sphere potential with all remaining h spheres. We focus on the region where the s sphere is larger than the h sphere, as measured by a parameter 1<α< 2 controlling the relative size of the two spheres. As α→ 2 a simple fluid of square-well spheres is recovered, whereas α→ 1 corresponds to the Janus dumbbell limit, where the h and s spheres have equal sizes. Many phase diagrams falling into three classes are observed, depending on the value of α. The 1.8 <α< 2...

Research paper thumbnail of Spontaneous dimensional reduction and novel ground state degeneracy in a simple chain model

Research paper thumbnail of From toroidal to rod-like condensates of semiflexible polymers

The competition between toroidal and rod-like conformations as possible ground states for DNA con... more The competition between toroidal and rod-like conformations as possible ground states for DNA condensation is studied as a function of the stiffness, the length of the DNA and the form of the long-range interactions between neighboring molecules, using analytical theory supported by Monte Carlo simulations. Both conformations considered are characterized by a local nematic order with hexagonal packing symmetry of neighboring DNA molecules, but differ in global configuration of the chain and the distribution of its curvature as it wraps around to form a condensate. The long-range interactions driving the DNA condensation are assumed to be of the form pertaining to the attractive depletion potential as well as the attractive counterion induced soft potential. In the stiffness-length plane we find a transition between rod-like to toroid condensate for increasing stiffness at a fixed chain length L. Strikingly, the transition line is found to have a L^1/3 dependence irrespective of the ...

Research paper thumbnail of Phase diagrams of Janus fluids with up-down constrained orientations

A class of binary mixtures of Janus fluids formed by colloidal spheres with the hydrophobic hemis... more A class of binary mixtures of Janus fluids formed by colloidal spheres with the hydrophobic hemispheres constrained to point either up or down are studied by means of Gibbs ensemble Monte Carlo simulations and simple analytical approximations. These fluids can be experimentally realized by the application of an external static electrical field. The gas-liquid and demixing phase transitions in five specific models with different patch-patch affinities are analyzed. It is found that a gas-liquid transition is present in all the models, even if only one of the four possible patch-patch interactions is attractive. Moreover, provided the attraction between like particles is stronger than between unlike particles, the system demixes into two subsystems with different composition at sufficiently low temperatures and high densities.

Research paper thumbnail of Chain stiffness bridges conventional polymer and bio-molecular phases

Chain molecules play important roles in industry and in living cells. Our focus here is on distin... more Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses – one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations including a coil, a globule, a toroid, rods, helices, zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffness play different physical roles ...

Research paper thumbnail of Local sequence‐structure relationships in proteins

Protein Science, 2021

We seek to understand the interplay between amino acid sequence and local structure in proteins. ... more We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the putative native state folds from myriad possible conformations? In order to address these questions, we represent the local structure of each Cα atom of a protein by just two angles, θ and μ, and we analyze a set of more than 4,000 protein structures from the PDB. We use a hierarchical clustering scheme to divide the 20 amino acids into six distinct groups based on their similarity to each other in fitting local structural space. We present the results of a detailed analysis of patterns of amino acid specificity in adopting local structural conformations and show that the sequence‐structure correlation is not very strong compared with a random assignment of sequence to structure. Yet, our analysis may be useful to determine an effective scoring rub...

Research paper thumbnail of Spontaneous dimensional reduction and ground state degeneracy in a simple chain model

Physical review. E, 2021

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new h... more Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first-order transition from a high-temperature random coil phase to a highly unusual low-temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures [we call these PoSSuM (Planar Structures with Secondary Motifs)] in the phase and protein native state structures.

Research paper thumbnail of Proteins — a celebration of consilience

International Journal of Modern Physics B, 2021

Proteins are the common constituents of all living cells. They are molecular machines that intera... more Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow from their native state structures and therefore understanding sequence-structure relationships is of fundamental importance. What is quite remarkable about proteins is that their understanding necessarily straddles several disciplines. The importance of geometry in defining protein native state structure, the constraints placed on protein behavior by mathematics and physics, the need for proteins to obey the laws of quantum chemistry, and the rich role of evolution and biology all come together in defining protein science. Here we review ideas from the literature and present an interdisciplinary framework that aims to marry ideas from Plato and Darwin and demonstrates an astonishing consilience between disciplines in describing proteins. We discu...

Research paper thumbnail of Computational pipeline to probe NaV1.7 gain-of-function variants in neuropathic painful syndromes

Scientific Reports, 2020

Applications of machine learning and graph theory techniques to neuroscience have witnessed an in... more Applications of machine learning and graph theory techniques to neuroscience have witnessed an increased interest in the last decade due to the large data availability and unprecedented technology developments. Their employment to investigate the effect of mutational changes in genes encoding for proteins modulating the membrane of excitable cells, whose biological correlates are assessed at electrophysiological level, could provide useful predictive clues. We apply this concept to the analysis of variants in sodium channel NaV1.7 subunit found in patients with chronic painful syndromes, by the implementation of a dedicated computational pipeline empowering different and complementary techniques including homology modeling, network theory, and machine learning. By testing three templates of different origin and sequence identities, we provide an optimal condition for its use. Our findings reveal the usefulness of our computational pipeline in supporting the selection of candidates f...

Research paper thumbnail of Proteins -- a celebration of consilience

arXiv (Cornell University), Nov 4, 2021

Proteins are the common constituents of all living cells. They are molecular machines that intera... more Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow from their native state structures and therefore understanding sequence-structure relationships is of fundamental importance. What is quite remarkable about proteins is that their understanding necessarily straddles several disciplines. The importance of geometry in defining protein native state structure, the constraints placed on protein behavior by mathematics and physics, the need for proteins to obey the laws of quantum chemistry, and the rich role of evolution and biology all come together in defining protein science. Here we review ideas from the literature and present an interdisciplinary framework that aims to marry ideas from Plato and Darwin and demonstrates an astonishing consilience between disciplines in describing proteins. We discuss the consequences of this framework on protein behavior.

Research paper thumbnail of Perturbation theory for the Percus-Yevick solution

Research paper thumbnail of Optimal channel networks: A framework for the study of river basin morphology

Water Resources Research, 1993

Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and glo... more Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and global rates of energy dissipation in a continuously fed (in space and time) plane aggregation system reminiscent, and based on the properties, of the planform of three-dimensional natural drainage networks. Geomorphological and fractal properties of OCNs are known from earlier studies by the authors. This paper explores further the structures derived by optimization of energy dissipation rates. Optimality of subnetworks and of basin shapes is investigated as a by-product of competition for drainage. A new perspective on the possible prediction of the width function of a basin network, and hence of its hydrologic response, is obtained by exploiting OCN techniques, requiting only the definition of the outer boundaries of the basin. The interplay between hillslope processes and the development of drainage networks is addressed, aiming at the relative role and the mutual interrelations of geology and optimal organization in the structure of mature fiver basins. Also addressed is the issue of multiscaling and multifractality in the spatial organization of the network. It is concluded that OCN approaches provide a comprehensive framework for the study of the morphology of geophysical structures. !. INTRODUCTION Important processes affect the planimetric structure of drainage basins. Chief among these are the development of channel links by headward growth and branching, migration of valleys and divides, capture processes, and adjustments of junction angles of confluent streams. It has been suggested that after an initial rudimentary drainage network is rapidly created upon strong influence of local topography and structural controls, a more regular, process-controlled, network is slowly formed [e.g., Howard, 1990]. The theoretical treatment of drainage network morphology has been dominated in the last 50 years by two approaches of different nature. One was based on deterministic rules, chiefly opti

Research paper thumbnail of Solvent quality and solvent polarity in polypeptides

Physical Chemistry Chemical Physics

Using molecular dynamics and thermodynamic integration, we report on the solvation process in wat... more Using molecular dynamics and thermodynamic integration, we report on the solvation process in water and in cyclohexane of seven polypeptides (GLY, ALA, ILE, ASN, LYS, ARG, GLU). The polypeptides are...

Research paper thumbnail of Potts-Submission

Research paper thumbnail of Equilibrium and linear transport properties of fluids-Fluids of spherical molecules with dipolarlike nonuniform adhesion: An analytically solvable anisotropic model

Physical Review-Section E-Statistical Nonlinear and Soft Matter Physics, 2008

Research paper thumbnail of Spontaneous dimensional reduction and novel ground state degeneracy in a simple chain model

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new h... more Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first order transition from a high temperature random coil phase to a highly unusual low temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures (we call these PoSSuM -- Planar Structures with Secondary Motifs) in the novel phase and protein native state structures.

Research paper thumbnail of Local symmetry determines the phases of linear chains: a simple model for the self-assembly of peptide

We discuss the relation between the emergence of new phases with broken symmetry within the frame... more We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric constraint that non-consecutive beads cannot overlap, and with a pairwise attractive square well potential accounting for the hydrophobic effect and promoting compaction. We then discuss the consequences of the successive breaking of spurious symmetries. First, we allow the partial interpenetration of consecutive beads. In addition to the standard high temperature coil phase and the low temperature collapsed phase, this results in a new class of marginally compact ground states comprising conformations reminiscent of α-helices and β-sheets, the building blocks of the native states of globular proteins. We then discuss the effect of a further symmetry breaking of the cylindrical symmetry on attaching a side-sphere to the backbone beads along the ne...

Research paper thumbnail of Bridging and depletion mechanisms in colloid-colloid effective interactions: A reentrant phase diagram

A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres ... more A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres represent the solvent and the solute, respectively, is introduced. The solute-solute and solvent-solvent interactions are of hard-sphere type, while the solute-solvent interactions are of sticky-hard-sphere type with tunable degrees of size nonadditivity and stickiness. Two particular and complementary limits are studied using analytical and semi-analytical tools. The first case is characterized by zero nonadditivity, lending itself to a Percus-Yevick approximate solution from which the impact of stickiness on the spinodal curves and on the effective solute-solute potential is analyzed. In the opposite nonadditive case, the solvent-solvent diameter is zero and the model can then be reckoned as an extension of the well-known Asakura-Oosawa model with additional sticky solute-solvent interaction. This latter model has the property that its exact effective one-component problem involves onl...

Research paper thumbnail of Theory and simulation studies of self-assembly of helical particle

This is the unedited authors' version of Chapter 3 appearing in the following book: Self-Asse... more This is the unedited authors' version of Chapter 3 appearing in the following book: Self-Assembly Systems: Theory and Simulations Ed. Li-Tang Yan John Wiley & Sons, Ltd, Chichester, pp. 53-84 (2017)

Research paper thumbnail of Left or right cholesterics? A matter of helix handedness and curliness

We have investigated the relationship between the morphology of helical particles and the feature... more We have investigated the relationship between the morphology of helical particles and the features of the cholesteric (N^∗ ) phase that they form. Using an Onsager-like theory, applied to systems of hard helices, we show that the cholesteric handedness and pitch depend on both the pitch and the curliness of the particles. The theory leads to the definition of pseudoscalars that correlate the helical features of the phase to the chirality of the excluded volume of the constituent particles.

Research paper thumbnail of Phase diagram of heteronuclear Janus dumbbells

Using Aggregation-Volume-Bias Monte Carlo simulations along with Successive Umbrella Sampling and... more Using Aggregation-Volume-Bias Monte Carlo simulations along with Successive Umbrella Sampling and Histogram Re-weighting, we study the phase diagram of a system of dumbbells formed by two touching spheres having variable sizes, as well as different interaction properties. The first sphere (h) interacts with all other spheres belonging to different dumbbells with a hard-sphere potential. The second sphere (s) interacts via a square-well interaction with other s spheres belonging to different dumbbells and with a hard-sphere potential with all remaining h spheres. We focus on the region where the s sphere is larger than the h sphere, as measured by a parameter 1<α< 2 controlling the relative size of the two spheres. As α→ 2 a simple fluid of square-well spheres is recovered, whereas α→ 1 corresponds to the Janus dumbbell limit, where the h and s spheres have equal sizes. Many phase diagrams falling into three classes are observed, depending on the value of α. The 1.8 <α< 2...

Research paper thumbnail of Spontaneous dimensional reduction and novel ground state degeneracy in a simple chain model

Research paper thumbnail of From toroidal to rod-like condensates of semiflexible polymers

The competition between toroidal and rod-like conformations as possible ground states for DNA con... more The competition between toroidal and rod-like conformations as possible ground states for DNA condensation is studied as a function of the stiffness, the length of the DNA and the form of the long-range interactions between neighboring molecules, using analytical theory supported by Monte Carlo simulations. Both conformations considered are characterized by a local nematic order with hexagonal packing symmetry of neighboring DNA molecules, but differ in global configuration of the chain and the distribution of its curvature as it wraps around to form a condensate. The long-range interactions driving the DNA condensation are assumed to be of the form pertaining to the attractive depletion potential as well as the attractive counterion induced soft potential. In the stiffness-length plane we find a transition between rod-like to toroid condensate for increasing stiffness at a fixed chain length L. Strikingly, the transition line is found to have a L^1/3 dependence irrespective of the ...

Research paper thumbnail of Phase diagrams of Janus fluids with up-down constrained orientations

A class of binary mixtures of Janus fluids formed by colloidal spheres with the hydrophobic hemis... more A class of binary mixtures of Janus fluids formed by colloidal spheres with the hydrophobic hemispheres constrained to point either up or down are studied by means of Gibbs ensemble Monte Carlo simulations and simple analytical approximations. These fluids can be experimentally realized by the application of an external static electrical field. The gas-liquid and demixing phase transitions in five specific models with different patch-patch affinities are analyzed. It is found that a gas-liquid transition is present in all the models, even if only one of the four possible patch-patch interactions is attractive. Moreover, provided the attraction between like particles is stronger than between unlike particles, the system demixes into two subsystems with different composition at sufficiently low temperatures and high densities.

Research paper thumbnail of Chain stiffness bridges conventional polymer and bio-molecular phases

Chain molecules play important roles in industry and in living cells. Our focus here is on distin... more Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses – one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations including a coil, a globule, a toroid, rods, helices, zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffness play different physical roles ...

Research paper thumbnail of Local sequence‐structure relationships in proteins

Protein Science, 2021

We seek to understand the interplay between amino acid sequence and local structure in proteins. ... more We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the putative native state folds from myriad possible conformations? In order to address these questions, we represent the local structure of each Cα atom of a protein by just two angles, θ and μ, and we analyze a set of more than 4,000 protein structures from the PDB. We use a hierarchical clustering scheme to divide the 20 amino acids into six distinct groups based on their similarity to each other in fitting local structural space. We present the results of a detailed analysis of patterns of amino acid specificity in adopting local structural conformations and show that the sequence‐structure correlation is not very strong compared with a random assignment of sequence to structure. Yet, our analysis may be useful to determine an effective scoring rub...

Research paper thumbnail of Spontaneous dimensional reduction and ground state degeneracy in a simple chain model

Physical review. E, 2021

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new h... more Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first-order transition from a high-temperature random coil phase to a highly unusual low-temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures [we call these PoSSuM (Planar Structures with Secondary Motifs)] in the phase and protein native state structures.

Research paper thumbnail of Proteins — a celebration of consilience

International Journal of Modern Physics B, 2021

Proteins are the common constituents of all living cells. They are molecular machines that intera... more Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow from their native state structures and therefore understanding sequence-structure relationships is of fundamental importance. What is quite remarkable about proteins is that their understanding necessarily straddles several disciplines. The importance of geometry in defining protein native state structure, the constraints placed on protein behavior by mathematics and physics, the need for proteins to obey the laws of quantum chemistry, and the rich role of evolution and biology all come together in defining protein science. Here we review ideas from the literature and present an interdisciplinary framework that aims to marry ideas from Plato and Darwin and demonstrates an astonishing consilience between disciplines in describing proteins. We discu...